Solutions of Pell’s Equation Involving Left Truncated Primes

Authors

  • V. A. Bindu * Department of Mathematics Rajagiri School of Engineering & Technology, Kakkanad, Cochin-682039, Kerala, India. https://orcid.org/0000-0001-5866-713X
  • Somanath Manju National College, (Affiliated to Bharathidasan University), Tiruchirappalli-620 002, Tamil Nadu, India.
  • Das Radhika Department of Mathematics Rajagiri School of Engineering & Technology, Kakkanad, Cochin-682039, Kerala, India.

https://doi.org/10.22105/opt.v2i4.91

Abstract

A Left-truncatable prime is a prime which in a given base (say 10) does not contain 0 and which remains prime when the leading (left) digit is successively removed. For example, 317 is left-truncatable prime since 317, 17 and 7 are all prime. Taking the cue from this initial research, we attempt to find the possible solutions for the Pell’s equation  for all choices of   In this paper, we focused primarily on Pell’s equations involving the left-truncatable primes and present to you another mysterious series and pattern typically associated with the Pell’s equation. As we proceed through the research, we will bring to the fore the recurrence relations among the identified solutions.

Keywords:

Pell’s equation, Diophantine equations, Integer solutions, Recurrence relation, Left truncated primes

References

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Published

2025-09-26

Issue

Vol. 2 No. 4 (2025): OPT

Section

Articles

How to Cite

Bindu, V. A., Manju, S. ., & Radhika, D. . (2025). Solutions of Pell’s Equation Involving Left Truncated Primes. Optimality, 2(4), 252-256. https://doi.org/10.22105/opt.v2i4.91